I wonder how different the perception of these projects being late or (massively) over budget would be if we used different words. Bear with me here...

Words mean things. Estimate carries a certain weight. It's almost scientific sounding. Instead, we should use the word "guess".

It's exactly equivalent, but imagine the outcome if everyone in the chain, from the very serious people involved in thinking up the project, to funding the project, to prioritising and then delivering the project, all used the word "guess"

Now, when the project is millions of dollars over budget and many months/years late, no one is under any pretence that it was going to be anything else.

I tried this once. It turns out serious people don't like the idea of spending millions of dollars based on "guessing", or even letting developers "play" in order to better understand the guesses they are forced to make, even when it turns un-educated guesses into educated guesses.

Of course, none of this would improve the outcome, but at least it sets expectations appropriately.